1. 7.2 GEOMETRIC Sequences

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pg # 1,2,3, 4,5abd, 6bdef, 7def, 9cd, 11, 12

3. REVIEW Sequence: an ordered list of numbers
Term: a number in a sequence (the first term is referred to as t1, the second term as t2, etc…)
example
3, 7, 11, 15, …
t1 = 3 t2 = 7 t3 = 11 t4 = 15

4. REVIEW - Recursive SEQUENCE
a sequence for which one or more terms are given
each successive term is determined by performing a calculation using the previous term(s)
example
t1 = describes 2, 6, 18, 54, …
tn =3 tn t2 =3t1 =3(2) = 6
n>1 , n  N t3 =3t2 =3(6) = 18

5. REVIEW - General term
a formula that expresses each term of a sequence as a function of its position
labelled tn
example
tn = 2n describes 2, 4, 6, 8, 10

6. REVIEW - arithmetic SEQUENCE
a sequence that has a common difference between any pair of consecutive terms
The general arithmetic sequence is a, a + d, a + 2d, a + 3d, …, where a is the first term and d is the common difference.
example
3, 7, 11, 15, … has a common difference of 4
7 – 3 = – 7 = – 11 = 4

7. REVIEW - Arithmetic sequence
General term
Recursive formula
tn = a + (n – 1)d
where
a is the first term
d is the common difference
n  N
t1 = a
tn = tn-1 + d
n > 1 , n  N

8. REVIEW - Arithmetic sequence
DISCRETE Linear function
f (n) = dn + b
where b = t0 = a - d

11. GEOMETRIC SEQUENCE
a sequence that has a common ratio between any pair of consecutive terms
the general geometric sequence is a, ar, ar2, ar3, …, where a is the first term and r is the common ratio
example
2, 6, 18, 54, … has a common ratio of 3
62=  6 =  18 = 3

12. t1 = a tn = rtn-1 n > 1 , n  N tn = ar n-1 GEOMETRIC SEQUENCES
General term
Recursive formula
tn = ar n-1
where
a is the first term
r is the common ratio
n  N
t1 = a
tn = rtn-1
n > 1 , n  N

13. GEOMETRIC SEQUENCES
DISCRETE EXPONENTIAL FUNCTION
f(n) = ar n-1

15. Example 1
State the common ratio and write the next three terms : a) 4, 8, 16, … b) -7.8, 3.8, –1.9, … c)

16. Example 2 tn = ar n-1 t1 = a, tn = rtn-1 n > 1
For each sequence, determine the general term, the recursive
formula and the indicated term.
5, 10, 20, … , t9
a, – 2ab, 4ab2, … , t17

17. Example 3 tn = ar n-1 t1 = a, tn = rtn-1 n > 1
Find the number of terms in each of the following geometric
sequences.
3, 6, 12, … , 768
567, 189, 63, … , 7/27

18. Example 4 tn = ar n-1 t1 = a, tn = rtn-1 n > 1
The 3rd term of a geometric sequence is 2 and the 10th term is . Determine the general term.

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pg # 1,2,3, 4,5abd, 6bdef, 7def, 9cd, 11, 12